Alexander von Humboldt

How to use this course

Alexander von Humboldt is often remembered as an explorer and a naturalist. That is accurate but incomplete. His expedition carried more than forty instruments, and he used them every day: barometers, thermometers, a dip needle, a cyanometer for the blue of the sky, an eudiometer for the composition of air. Out of these numbers he built new sciences. He measured how the strength of the Earth’s magnetic field changes with latitude, drew the first map of isotherms, showed quantitatively how vegetation changes with altitude, and organised the first worldwide network of simultaneous magnetic observations.

Each technical lesson opens with a paragraph for the general reader, then states the physics precisely, works through Humboldt’s own data where we have them, and ends with exercises with folded solutions. We distinguish what Humboldt measured from the theory later physicists built on his measurements, much of it by Carl Friedrich Gauss.

Timeline

Berlin and Tegel, 1769–1789

Alexander von Humboldt was born in Berlin on 14 September 1769. His father, Alexander Georg von Humboldt, was a former army major and chamberlain at the Prussian court; his mother, Maria Elisabeth Colomb, came from a Huguenot family and brought wealth from her first marriage, including the estate at Tegel outside Berlin. The Duke of Brunswick was Alexander’s godfather. His only full sibling, Wilhelm, two years older, became a statesman, the founder of the University of Berlin and a pioneer of linguistics.

The father died in 1779. The mother, reserved and ambitious, gave the boys the best private tutors in Berlin, aiming them at careers in the Prussian state. Their teachers included the physician and Kantian philosopher Marcus Herz, who lectured to them on physics and philosophy, and later the botanist Carl Ludwig Willdenow, who drew Alexander into collecting plants. Wilhelm was the scholar of the two. Alexander was restless, often unwell as a child, and happiest outdoors, collecting insects, plants and stones.

In 1787 the brothers spent a semester at the small university of Frankfurt an der Oder, where Alexander was supposed to study finance and administration. He spent the following year in Berlin studying technology, botany and Greek. By 1789 he knew he wanted a life in natural science, and the obvious place to begin was the University of Göttingen.

Göttingen, Freiberg and the mines, 1789–1798

Humboldt matriculated at Göttingen on 25 April 1789. He heard the anatomist Johann Friedrich Blumenbach and the classicist Christian Gottlob Heyne, and he attended the physics lectures of Georg Christoph Lichtenberg, the leading experimental physicist in Germany. On a trip to the Rhine he studied basalts, and his first book (1790) argued, following his later teacher Werner, that basalt was a sediment. He would abandon that view when he saw volcanoes.

Forster

In Mainz he met Georg Forster, who had sailed round the world with James Cook. In 1790 the two travelled together through the Netherlands to London, where Humboldt met Joseph Banks, and then to Paris, then in the first year of the Revolution. Forster showed him that a scientific traveller could also write vividly about landscape and people. Humboldt later said the journey with Forster decided the direction of his life.

Mining officer

After a term at the commercial academy in Hamburg, he went in June 1791 to the Bergakademie in Freiberg, Saxony, the best mining school in Europe, and studied under the geologist Abraham Gottlob Werner. He finished the programme in eight months. In March 1792 he entered the Prussian mining service, and within months was chief mining officer for the Franconian principalities of Bayreuth and Ansbach. He worked hard and practically: he founded a free school for miners, wrote its textbooks, analysed the bad air in mines, designed safety lamps that would burn in it, and built a respirator. Testing them underground, he once passed out from mine gas. His first botanical book, Florae Fribergensis (1793), described the mosses and fungi growing in the dark of the mines.

In these years he also became close to Johann Wolfgang von Goethe and Friedrich Schiller in Jena and Weimar, and he carried out several thousand experiments on galvanism, many on his own body (Lesson 09). His mother died in November 1796. The inheritance made him rich and free. He left the mining service and began planning a great scientific journey.

The American journey, 1799–1804

In Paris in 1798 Humboldt met the young botanist Aimé Bonpland. A French round-the-world expedition he hoped to join was cancelled, and attempts to reach Egypt failed. The two went to Madrid, where in March 1799 King Charles IV granted Humboldt the rare permission to travel freely in Spanish America at his own expense.

They sailed from La Coruña on the Pizarro on 5 June 1799, climbed the Pico del Teide on Tenerife, and landed at Cumaná, Venezuela, on 16 July. Humboldt’s instruments came too: chronometer and sextant for position, barometers for altitude, thermometers and hygrometers, a dip needle and a declination compass, an eudiometer, a cyanometer. On the night of 11–12 November 1799 at Cumaná they watched thousands of meteors, the Leonid storm, and Humboldt recorded it carefully (Lesson 10).

Orinoco and Andes

In 1800 they spent about four months travelling by canoe up the Orinoco and confirmed the existence of the Casiquiare, a natural channel joining the Orinoco and Amazon basins. At Calabozo they studied electric eels, and Humboldt took severe shocks. After a stay in Cuba they went to Cartagena and up the Magdalena to Bogotá, where they met the botanist José Celestino Mutis, and then across the Andes to Quito, which they reached in January 1802.

On 23 June 1802, with Bonpland and the young Ecuadorian Carlos Montúfar, Humboldt climbed Chimborazo, then believed the highest mountain in the world. A gap in the ridge stopped them some hundreds of metres below the summit (6263 m), at a height he estimated at about 5 900 m, a record for climbers for some thirty years. In northern Peru he located the point where the magnetic dip vanished, the magnetic equator, and at Callao on the coast he measured the cold water of the current that now bears his name, and observed the transit of Mercury of 9 November 1802.

They spent 1803 in Mexico, in the archives, observatories and silver mines, then returned through Cuba to Philadelphia and Washington, where Humboldt met President Thomas Jefferson. He landed at Bordeaux on 3 August 1804, with some 60 000 plant specimens and notebooks full of numbers.

Magnetic intensity and the dip needle

For the general reader. A compass shows the direction of the Earth’s magnetic field. Humboldt asked how strong the field is, and whether its strength changes from place to place. He swung a magnetised needle like a pendulum and counted its oscillations: the stronger the field, the faster it swings. Over five years and thousands of kilometres he found that the field weakens steadily from the poles toward the magnetic equator.

The oscillation method

A magnetised needle of moment \(m\) and moment of inertia \(I\), free to swing about its centre in the plane of the field \(B\), feels a restoring torque \(-mB\sin\theta\). For small angles it oscillates harmonically.

The method gives only ratios, because \(m\) and \(I\) are unknown and \(m\) may drift as the needle ages. Humboldt therefore expressed all intensities relative to his value at the magnetic equator in northern Peru, taken as 1. This scale was the standard for three decades, until Gauss found a way to measure intensity absolutely (Lesson 05). In the memoir that Humboldt and Jean-Baptiste Biot presented to the Institut in Paris in December 1804, the same needle that made 245 oscillations in ten minutes in Paris made only 211 in Peru.

The field of a dipole

To first approximation the Earth’s field is that of a dipole of moment \(M\) at its centre. In spherical coordinates with \(r\) the distance from the centre and \(\lambda\) the magnetic latitude,

Both follow at once from the components above: \(\tan I=|B_r/B_\lambda|=2\tan\lambda\) and \(F^2=B_0^2(4\sin^2\lambda+\cos^2\lambda)\). Biot compared Humboldt’s data with the field of a small magnet near the centre of the Earth and found rough agreement. The departures are as interesting as the agreement, as the next exercise shows.

Magnetic storms and the global network

For the general reader. In Berlin in 1806–07 Humboldt watched a compass needle through a microscope, sometimes every hour for days and nights. During a display of the northern lights the needle shook wildly. He called the event a “magnetic storm” and realised that to understand such storms, observers in many places would have to watch at the same moments. He spent decades building that network, and recruited Gauss to supply the theory.

From Berlin to the world

With the astronomer Jabbo Oltmanns, Humboldt recorded the declination of a suspended magnet in Berlin from May 1806 to June 1807. On 21 December 1806, during a bright aurora, the needle became erratic for hours. Humboldt named such disturbances magnetische Ungewitter, magnetic storms. After returning to Berlin in 1827 he had an iron-free magnetic hut built and arranged for observers in other cities to read their instruments at agreed times. In 1828 he hosted the meeting of German natural scientists in Berlin, and Carl Friedrich Gauss stayed in his house. Humboldt urged him to take up magnetism.

Gauss did, with the physicist Wilhelm Weber. In 1832 Gauss showed how to measure the horizontal intensity in absolute units of length, mass and time, by combining the oscillation period of a magnet with its deflection of a second needle. In the mid-1830s Gauss and Weber organised the Göttingen Magnetic Union, whose stations observed at the same Göttingen times on agreed days. In April 1836 Humboldt wrote to the Duke of Sussex, President of the Royal Society, asking Britain to establish stations across its empire. The resulting “magnetic crusade”, led by Edward Sabine, set up observatories from Toronto to Tasmania, while Russia built a chain across Siberia. By the early 1840s the data showed that magnetic storms are global, and Sabine later linked their frequency to the sunspot cycle.

Gauss’s theory (1839)

Outside its sources, the magnetic field is curl-free, so \(\mathbf B=-\nabla V\), and since \(\nabla\cdot\mathbf B=0\), the potential satisfies Laplace’s equation.

The axial dipole term is \(V_1=a\,g_1^0\,(a/r)^2\cos\theta\), giving at the surface \(B_r=2g_1^0\cos\theta\) and \(B_\theta=g_1^0\sin\theta\). Comparing with Lesson 04 gives \(|g_1^0|=B_0=\mu_0M/(4\pi a^3)\). The modern value is about \(g_1^0\approx-29\,400\) nT; Gauss’s own analysis gave a larger dipole, and the dipole has weakened by some 9% since his time.

Isotherms and the climate of continents

For the general reader. Paris lies farther north than Quebec, yet Quebec is much colder. Climate does not follow latitude alone. In 1817 Humboldt collected mean temperatures from stations around the Northern Hemisphere, joined places of equal mean temperature with curves, and published the first isotherm map. The curves bend: north over western Europe, south over eastern North America and Asia. Every weather map with isotherms descends from it.

Humboldt’s 1817 memoir

Des lignes isothermes et de la distribution de la chaleur sur le globe appeared in the memoirs of the Société d’Arcueil, the circle of Pierre-Simon Laplace and Claude-Louis Berthollet. Humboldt warned that the mean of the year’s highest and lowest readings is a poor estimate of mean temperature, and recommended several readings a day. He compared mean annual temperatures in western Europe and eastern America at the same latitudes:

He also drew lines of equal summer and of equal winter temperature, and found that winter lines depart from the parallels of latitude far more than summer lines. Places with the same mean annual temperature differ in latitude by at most some 8–9°, while places with the same winter mean may differ by 18–19°.

Why west coasts are mild: a toy model

Humboldt attributed the mild west-coast winters to the prevailing westerly winds blowing off the ocean, and to the ocean’s capacity to store heat. A linear energy balance makes the second point quantitative. Let a column with heat capacity \(C\) per unit area receive a seasonally varying net heating \(F_0\cos\omega t\) and lose heat at the rate \(\lambda T'\), where \(T'\) is the departure from the annual mean:

Substitute \(T'=\mathrm{Re}(\hat T e^{i\omega t})\) to get \((\lambda+iC\omega)\hat T=F_0\); the modulus and argument of \(\hat T\) give \(A\) and \(\varphi\). Winds carry the ocean’s damped climate inland on west coasts; on east coasts the winds come off the continent.

Height, pressure and the lapse rate

For the general reader. Humboldt measured the heights of mountains, plateaus and passes with a barometer: the higher you go, the lower the pressure. He also recorded temperature at every height and found that it falls by a few degrees per kilometre. At the equator the snow line lies near 5 km; in the Alps, much lower. Height and latitude play similar roles in climate.

Dividing the hydrostatic equation by \(p\) gives \(d\ln p/dz=-\mu g/(RT)\), which integrates to the formula. Barometric levelling in Humboldt’s time used this law with corrections for the mean temperature of the air column and for the expansion of mercury.

For an adiabatic change of an ideal gas, \(c_p\,dT=dp/\rho\) per unit mass (the first law with \(dq=0\)). With \(dp=-\rho g\,dz\), this gives \(c_p\,dT=-g\,dz\). Condensation of water vapour releases latent heat, so moist air cools more slowly. The observed mean tropospheric lapse rate is about 6.5 K/km.

Plant geography and the Tableau physique

For the general reader. On the slopes of the Andes, Humboldt saw the vegetation change with height: palms and bananas at the bottom, oaks and tree ferns higher up, then grasslands, then lichens below the snow. He drew a single picture of a volcano with the plants written in at their heights and columns of numbers alongside: temperature, pressure, humidity, the boiling point of water, the blue of the sky. It founded the science of plant geography.

The Essai (1807)

The Essai sur la géographie des plantes, written with Bonpland and published in Paris in 1807 (with a German edition dedicated to Goethe), was the first volume of the expedition’s results. Its centrepiece, the Tableau physique des Andes et pays voisins, shows a cross-section of Chimborazo with Cotopaxi behind it. Plant names are written inside the mountain at the heights where they grow. Side columns give, against altitude, the temperature, the decrease of gravity, the cyanometer reading of the sky’s blueness, the humidity, the electrical tension of the air, the heights of other mountains for comparison, and the limits of cultivation and of snow.

These principles underlie modern biogeography, ecology and the study of how climate change moves species. Charles Darwin carried Humboldt’s Personal Narrative on the Beagle.

A modern resurvey

In 2015 a team resurveyed Chimborazo and compared their plant limits with the Tableau, concluding that the upper limit of vegetation had risen by more than 500 m. In 2019 Pierre Moret and colleagues, working from Humboldt’s diaries, showed that much of the high-altitude plant data in the Tableau was actually collected on another volcano, Antisana, and that Humboldt revised his figures later in works that were less widely read. Historical data, however famous, have to be read with their provenance.

Galvanism and the analysis of air

For the general reader. In the 1790s scientists argued over Luigi Galvani’s twitching frogs’ legs: was the electricity in the animal, or in the metals touching it? Humboldt did thousands of experiments, many on wounds he made in his own back. Later, with Joseph Louis Gay-Lussac, he measured the oxygen in air with great accuracy and found that hydrogen and oxygen combine in a two-to-one ratio by volume.

Galvanism (1797)

Galvani held that animal tissue produces electricity; Alessandro Volta argued that the contact of two different metals produces it and the frog’s leg only detects it. Humboldt’s two-volume Versuche über die gereizte Muskel- und Nervenfaser (1797) reported thousands of trials, some pointing to electricity in the animal and others to the metals. Both sides were partly right. Volta’s pile of 1800 settled the question of metallic contact, while nerve conduction turned out to be electrical too. In 1800 in Venezuela Humboldt tested electric eels directly.

Eudiometry (1805)

A Volta eudiometer is a graduated glass tube over water. A measured volume of air is mixed with hydrogen and a spark is passed; the oxygen combines with hydrogen to form water, which condenses, and the gas volume shrinks.

Humboldt and Gay-Lussac established the 2 : 1 ratio with care and found that the oxygen content of air is about 21% and essentially constant from place to place. Gay-Lussac generalised the simple volume ratios in 1808 into his law of combining volumes, one of the supports of Amedeo Avogadro’s hypothesis of 1811.

The Cosmos programme

For the general reader. Humboldt believed that nature is one connected whole, and that the connections show up in numbers measured carefully, in many places, and compared. His great book Kosmos tried to describe the whole physical universe, from nebulae to mosses, in this spirit. Historians call this style of research Humboldtian science: precise instruments, global networks, mean values, and maps of physical quantities.

The programme

Kosmos grew out of 61 lectures Humboldt gave at the University of Berlin from November 1827 to April 1828, and a parallel series of 16 public lectures at the Sing-Akademie, open to all and with about a thousand seats. The book appeared in volumes from 1845. Volume 1 is a general portrait of nature from the heavens to the Earth; volume 2 a history of how people have perceived and studied nature; volumes 3 and 4 treat astronomy and the physics of the Earth in detail, including terrestrial magnetism, volcanoes and earthquakes. A fifth volume was left unfinished at his death.

The proviso is the whole art. Humboldt’s warnings about max–min means (Lesson 06) and Gauss’s insistence on simultaneous observations (Lesson 05) are ways of keeping errors independent and unbiased.

The Leonids

On 12 November 1799 at Cumaná, Humboldt and Bonpland saw thousands of meteors. After a great Leonid storm over North America in November 1833, astronomers comparing records recognised Humboldt’s 1799 account as an earlier storm of the same shower. The interval suggested a period of about 33 years, later identified with the orbit of the comet Tempel–Tuttle.

Paris, Berlin and Siberia, 1804–1840

Humboldt returned to Europe a celebrity. He chose to live in Paris, the scientific capital, rather than Berlin. There he worked with Gay-Lussac, with whom he travelled to Italy in 1805, and formed a lifelong friendship with François Arago. With Bonpland and later Carl Sigismund Kunth on the botany, and with collaborators in astronomy, zoology and geography, he published the results of the expedition in some thirty volumes over more than two decades, at enormous cost to his fortune. They included the Political Essay on the Kingdom of New Spain, the first scientific description of Mexico, and the Personal Narrative that inspired Darwin. He became a patron of younger scientists, introducing Justus von Liebig to Gay-Lussac in 1822 and helping Peter Gustav Lejeune Dirichlet return to Prussia in 1826.

Berlin

By the mid-1820s his money was gone, and the Prussian king required his chamberlain to live at court. In 1827 Humboldt moved back to Berlin. He gave the Kosmos lectures that winter, organised the 1828 meeting of German natural scientists, began his magnetic network, and used his influence with the crown to support mathematicians and scientists, among them Dirichlet, Carl Gustav Jacob Jacobi, Jakob Steiner and later Hermann von Helmholtz.

Russia, 1829

Invited and financed by Tsar Nicholas I, Humboldt crossed the Russian empire in 1829, from St Petersburg through Moscow, Kazan and Yekaterinburg to the Altai and the Chinese border, returning by the Caspian. He was 59. He measured magnetism, temperature and altitude along the way and, on his return, urged the Russian government to establish magnetic and meteorological stations across the empire; a chain of them followed. His Asie centrale (1843) reported the results.

Kosmos, death and legacy, 1840–1859

In his seventies and eighties Humboldt worked late into the night on Kosmos, answering thousands of letters a year. The first volume (1845) sold out within weeks and was translated into most European languages. In 1842 King Frederick William IV founded the civil class of the Pour le Mérite order for sciences and arts, and made Humboldt its chancellor; he used it to honour scientists such as Gauss and Dirichlet. The Royal Society awarded him the Copley Medal in 1852.

He died at his home in Berlin on 6 May 1859, aged 89, having just finished the manuscript of volume 4 and begun volume 5. He received a state funeral and was buried in the family tomb at Tegel. The centenary of his birth in 1869 was celebrated across Europe and the Americas.

Legacy

• Geomagnetism: the first systematic data on magnetic intensity and the magnetic equator; the discovery and naming of magnetic storms; the global network of simultaneous observations that made Gauss’s theory possible.
• Climatology: isotherms and the method of mapping mean values; the contrast of maritime and continental climates; temperature against altitude.
• Biogeography and ecology: vegetation zones, the altitude–latitude analogy, and the study of plants as part of a physical environment.
• Scientific style: precise instruments carried into the field, international cooperation, and graphical presentation of data.
• Names: the Humboldt Current, the Humboldt penguin and squid, Humboldt Glacier in Greenland, the lunar Mare Humboldtianum, many towns and counties, and the Alexander von Humboldt Foundation, which since 1953 in its present form has brought researchers to Germany.

Humboldt never married, and lived for his work. He opposed slavery all his life and wrote against it in his essay on Cuba. He was generous to younger scientists, vain about his own priority, and tireless. His influence on nineteenth-century science was so pervasive that it became almost invisible.

Connections

People linked to Alexander von Humboldt across this collection. A name without a link has no page here yet. See Alexander von Humboldt in the network of all 337 lives →

Teachers and advisors

• Abraham Gottlob Werner 1791-1792
• Johann Friedrich Blumenbach 1789-1790

Influenced by

• Luigi Galvani
• Georg Christoph Lichtenberg 1789-1790
• Georg Forster 1790

Influenced

• Charles Darwin

Colleagues and collaborators

• Alessandro Volta
• Carl Friedrich Gauss 1828-1855
• Carl Gustav Jacob Jacobi
• Hermann von Helmholtz
• Jakob Steiner
• Jean-Baptiste Biot 1804
• Joseph Louis Gay-Lussac 1805-1806
• Justus von Liebig
• Peter Gustav Lejeune Dirichlet
• Wilhelm Weber
• Aimé Bonpland 1798-1807
• Edward Sabine

Friends

• Caroline Herschel
• François Arago
• Jakob Steiner
• Justus von Liebig
• Peter Gustav Lejeune Dirichlet
• Johann Wolfgang von Goethe

Family

• Wilhelm von Humboldt

Also mentioned in this life

• Amedeo Avogadro
• Pierre-Simon Laplace
• Adrien-Marie Legendre

Fields

• geomagnetism 3 lives

Sources and further reading

Biography

1. Alexander von Humboldt, Wikipedia (English); German edition.
2. Alexander von Humboldt, MacTutor History of Mathematics.
3. A. Wulf, The Invention of Nature: Alexander von Humboldt’s New World, Knopf, 2015.
4. L. Kellner, Alexander von Humboldt, Oxford University Press, 1963.
5. Der Humboldt’sche Magnetische Verein im historischen Kontext, HiN – Alexander von Humboldt im Netz.
6. Alexander von Humboldt und Carl Friedrich Gauß als Wegbereiter der neuen Disziplin Erdmagnetismus, HiN.

Science

1. A. von Humboldt and J.-B. Biot, On the variations of the terrestrial magnetism in different latitudes (1804), Bern digital edition.
2. A. von Humboldt, Of isothermal lines, and the distribution of heat over the globe (1817; English 1818), Bern digital edition.
3. A. von Humboldt and A. Bonpland, Essai sur la géographie des plantes, Paris, 1807. English: Essay on the Geography of Plants, ed. S. T. Jackson, University of Chicago Press, 2009.
4. A. von Humboldt, Kosmos, 5 vols., 1845–1862.
5. C. F. Gauss, Allgemeine Theorie des Erdmagnetismus, in Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1838, Leipzig, 1839.
6. P. Moret et al., Humboldt’s Tableau Physique revisited, PNAS 116 (2019); Science News report.
7. Magnetic storms and the first observatories, NASA From Stargazers to Starships.
8. Geomagnetic storm, Wikipedia (history section).
9. Carte des lignes isothermes (1817), University of Denver copy.